Which one of the following has different number of molecules ? (All are kept at normal temperature and pressure)
- (a)3 gram of Hydrogen
- (b)48 gram of Oxygen
- (c)42 gram of Nitrogen
- (d)2 gram of Carbon
Correct — D, 2 gram of Carbon. The count of particles in a sample depends on the number of moles, and moles are found by dividing the mass by the molar mass. Hydrogen gas is H2 with a molar mass of 2, so 3 g gives 1.5 mol. Oxygen gas is O2 with a molar mass of 32, so 48 g gives 1.5 mol. Nitrogen gas is N2 with a molar mass of 28, so 42 g gives 1.5 mol. Three of the four samples therefore hold the same number of particles, about 9.03 × 10^23 each. Carbon has an atomic mass of 12, so 2 g is only one-sixth of a mole, roughly 1.0 × 10^23 particles — about a ninth of what the others hold. There is a second reason carbon is the odd one here, worth knowing even though the arithmetic already settles the answer: at ordinary temperature carbon is a solid built as a continuous network of atoms, not a gas made of separate molecules, so it stands apart from the three diatomic gases in kind as well as in count.
- (a)3 gram of Hydrogen — Hydrogen gas is diatomic, H2, with a molar mass of 2 g per mole, so 3 g is exactly 1.5 mol — the same as options (b) and (c). Treating hydrogen as atomic with a mass of 1 would give 3 mol and wrongly single this option out.
- (b)48 gram of Oxygen — Oxygen gas is O2 with a molar mass of 32 g per mole, and 48 divided by 32 is 1.5 mol, matching the others. The large mass figure makes it look like the outlier, but molar mass is large to match.
- (c)42 gram of Nitrogen — Nitrogen gas is N2 with a molar mass of 28 g per mole, and 42 divided by 28 is again 1.5 mol. Every one of the three gases has been sized to give the same answer.
The mole is chemistry's counting unit: one mole of anything contains 6.022 × 10^23 particles, a figure called the Avogadro constant. The mass of one mole in grams is numerically equal to the molecular or atomic mass, so mass divided by molar mass gives the number of moles, and moles multiplied by the Avogadro constant gives the number of particles. Avogadro's law adds the companion idea for gases: equal volumes at the same temperature and pressure hold equal numbers of molecules.
Questions of this design are answered by converting every option to moles before comparing anything. Three of the four figures will match and the fourth will not, so once two options agree you know what number you are looking for. The most frequent error here is forgetting that hydrogen, oxygen and nitrogen exist as diatomic molecules, and dividing by 1, 16 and 14 instead of 2, 32 and 28. Doing that makes all three gases come out at 3 mol, which is still equal, so the answer would not change — but the same slip does change the answer in many other questions, so fix the habit now.
- One mole of any substance contains 6.022 × 10^23 particles, the Avogadro constant.
- The number of moles equals the mass divided by the molar mass.
- Hydrogen, oxygen and nitrogen all occur as diatomic gases, with molar masses of 2, 32 and 28 g per mole.
- 3 g of hydrogen, 48 g of oxygen and 42 g of nitrogen are each 1.5 mol, while 2 g of carbon is one-sixth of a mole.
- Avogadro's law states that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.
Three samples come to 1.5 mol each; only the carbon differs.
- Treating hydrogen, oxygen and nitrogen as single atoms instead of diatomic molecules.
- Comparing masses directly instead of converting each sample to moles first.
Mole arithmetic is a standing NDA GAT item, usually one calculation per paper, and it is almost always solvable in under a minute once every quantity is turned into moles.
Which one of the following is the correct sequence in increasing order of molecular weights of the hydrocarbons?
- (a) Methane, ethane, propane and butane
- (b) Propane, butane, ethane and methane
- (c) Butane, ethane, propane and methane
- (d) Butane, propane, ethane and methane
Answer(a) Methane, ethane, propane and butane
Rests on the same skill of building a molar mass from a formula, which is the step that turns each option in this question into a number of moles.
The proposition ‘equal volumes of different gases contain equal numbers of molecules at the same temperature and pressure’ is known as
- (a) Avogadro’s hypothesis
- (b) Gay-Lussac’s hypothesis
- (c) Planck’s hypothesis
- (d) Kirchhoff’s theory
Answer(a) Avogadro’s hypothesis
Names the law behind the whole idea of counting molecules by amount rather than by mass, and it is the companion result to the mole arithmetic used here.
- practice — not a real PYQ
How many molecules are present in 8 g of oxygen gas at ordinary conditions?
- (a)6.022 × 10^23
- (b)3.011 × 10^23
- (c)1.505 × 10^23
- (d)12.044 × 10^23
Answer(c) 1.505 × 10^23 — 8 g of O2 is a quarter of a mole, since the molar mass is 32.
- practice — not a real PYQ
Equal masses of which pair of gases contain the same number of molecules?
- (a)Hydrogen and oxygen
- (b)Nitrogen and carbon monoxide
- (c)Oxygen and nitrogen
- (d)Helium and neon
Answer(b) Nitrogen and carbon monoxide — both have a molar mass of 28, so equal masses mean equal moles.